Penn EM.
The Banks Set in Infinite Spaces. Social Choice and Welfare. 2006.
AbstractI provide a definition of the Banks set, or set of sophisticated voting outcomes, over an infinite policy space and when individual preferences are weak. I also show that the Banks set is a subset of one definition of the uncovered set, but not another. The interpretation of the Banks set in this setting differs from Banks’s original interpretation in the implicit role of the agenda setter. In addition, a characterization of the Banks set is provided for a three-player game of distributive politics. In this special setting, the Banks set and all definitions of the uncovered set have full measure over the space of alternatives.
The_Banks_Set_in_Infinite_Spaces.pdf Penn EM.
Alternate definitions of the uncovered set, and their implications. Social Choice and Welfare. 2006.
AbstractDifferent definitions of the uncovered set are commonly, and often interchangeably, used in the literature. If we assume individual preferences are strict over all alternatives, these definitions are equivalent. However, if one or more voters is indifferent between alternatives these definitions may not yield the same uncovered set. This note examines how these definitions differ in a distributive setting, here each voter can be indifferent between any number of alternatives. I show that, defined one way, the uncovered set is equal to the set of Pareto allocations that give over half the voters a strictly positive payoff, while alternate definitions yield an uncovered set that is equal to the entire Pareto set. These results highlight a small error in Epstein (1998) in which the author characterizes the uncovered set for a different definition of covering than claimed.
Alternate_definitions_of_the_uncovered_set_and_their_implications.pdf